Mensuration and CalculationAQA GCSE Maths: Revision notes

You must know and apply formulae to calculate the areas of:

• Triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
• Parallelogram: $\text{Area} = \text{base} \times \text{height}$
• Trapezium: $\text{Area} = \frac{1}{2}(a+b)h$, where $a$ and $b$ are the parallel sides

Perimeter is the total distance around the outside of a shape — add all the side lengths together. Standard units of measure (length, area, volume/capacity, mass, time, money) must be used and applied correctly, including in geometrical problems set on coordinate axes.

Know the formulae:

• Circumference: $C = 2\pi r = \pi d$
• Area: $A = \pi r^2$

These can be used to find the perimeter of composite 2D shapes involving circles, and the area of circles and composite shapes (shapes made of more than one basic shape). Answers may be required in terms of $\pi$ (i.e. left with $\pi$ in the answer rather than as a decimal).

A sector is a 'slice' of a circle between two radii, and an arc is the curved part of its boundary. Given the angle $\theta$ at the centre:

• Arc length $= \frac{\theta}{360} \times 2\pi r$
• Sector area $= \frac{\theta}{360} \times \pi r^2$

At Higher tier, this extends to frustums — a cone or pyramid with the top cut off parallel to the base.

You must be able to calculate:

• Volumes of cuboids and other right prisms, including cylinders — volume of a prism $=$ cross-sectional area $\times$ length
• Surface area and volume of spheres, pyramids and cones, and composite solids built from combinations of these

Apply the correct formula depending on what the problem asks for, and use consistent units throughout.